Again, I am having trouble proving what I keep getting right by using by subconscious logic.
For the problem:
a_1 = 2, a_(n+1) = (5n+1)/(4n+3) * a_n ==> Does this converge (absolutely or conditionally) or diverge?
What I did was:
the limit of (5n+1)/(4n+3) as n->inf = 5/4 therefore you will be adding increaing numbers and that means the sum will be infinite. Also, to try to prove this, I wrote that when n>=2, 5n+1 >= 4n+3 to show that I am always multiplying the previous number by something equal to or larger than 1 since the sum starts at 2 due to a_1 being predetermined.
If someone could please help me get my thoughts into mathematical writing then it would be greatly appreciated!
Thanks in advance!